Rounding Methods for Discrete Linear Classification (Extended Version)

Yann Chevaleyre (1) , Frederic Koriche (2) , Jean-Daniel Zucker (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 CRIL - Centre de Recherche en Informatique de Lens
3 IRD - Institut de Recherche pour le Développement

Learning discrete linear classifiers is known as a difficult challenge. In this paper, this learning task is cast as combinatorial optimization problem: given a training sample formed by positive and negative feature vectors in the Euclidean space, the goal is to find a discrete linear function that minimizes the cumulative hinge loss of the sample. Since this problem is NP-hard, we examine two simple rounding algorithms that discretize the fractional solution of the problem. Generalization bounds are derived for several classes of binary-weighted linear functions, by analyzing the Rademacher complexity of these classes and by establishing approximation bounds for our rounding algorithms. Our methods are evaluated on both synthetic and real-world data.

Mots clés: linear classification; convex relaxation; binary weights

Domaines: Apprentissage [cs.LG]

Yann Chevaleyre, Frederic Koriche, Jean-Daniel Zucker. Rounding Methods for Discrete Linear Classification (Extended Version). 2013. ⟨hal-00771012v2⟩